An adult wonders whether road curvature accounts for the different speeds reported
by her cruise control and by the highway patrolman who pulled her over. After
distinguishing between speed and angular velocity, Doctor Carter calculates
gravitational accelerations to model the event and check the plausibility of the data.

A cake is square when viewed from the top. Height is unspecified. It is
iced on top and the four vertical sides. How can the cake be divided in 5
pieces such that each piece has the same amount of cake and the same
amount of icing? How can you minimize the number of cuts you have to make
in the cake and still meet this target? Alternatively, how can you
minimize the total length of the cuts you make in the cake?

In the end elevation of a drawing, a rod rises from point A at 32
degrees. In the side elevation, the same rod is seen rising from point
A at 48 degrees. How do I work out at what angle to cut the end of the
rod?

Is there a mathematical formula to determine the length of material on
a roll, given the outside diameter of the core, the outside diameter
of the whole roll, and the thickness of the material (determined by a
micrometer)?

I want to have my students draw a scale model of the solar system that
shows the orbits of the planets. Assuming I have the apogee and
perigee of each planet's orbit about the sun, they need to construct 9
ellipses with some degree of accuracy. What's the best way to go about
this?

I have solar collectors on my roof. They are mounted so that the base
of each panel runs up the slope of the roof, and the panels themselves
are mounted at an angle. I'd like to know how to determine the various
angles created by this situation.

If I can see the end of a roll of carpet I can figure out the
approximate square yardage by taking the inside circumference, the
outside circumference and the number of total layers left, then
calculating each layer. Is there a formula I can apply to calculate
the result directly?

A pipe has become bent and is no longer round. In order for me to correct
the problem, I must build a brace to go around the pipe and true it up.
However, until I can determine the radius of the pipe, a brace cannot be
built.

A pool's surface forms a rectangle 25 meters long by 15 meters wide. The
pool is 2 meters deep at the shallow end and the depth increases at the
constant rate to four meters at the other end. How many liters of water
will the pool hold?